Histories Without Collapse

Miguel Centeno, Peter Callahan, Paul A. Larcey +1 more

Leonardo Castellani

We argue that Wigner's friend thought experiment does not support observer dependence of quantum states. An analysis in terms of history vectors suggests that quantum collapse is to be understood as collapse of histories rather than collapse of states.

Fay Dowker B, Yousef Ghazi-Tabatabai

The structure of collapse models is investigated in the framework of quantum measure theory, a histories-based approach to quantum mechanics. The underlying structure of coupled classical and quantum systems is elucidated in this approach which puts both systems on a spacetime footing. The nature of the coupling is exposed: the classical histories have no dynamics of their own but are simply tied, more or less closely, to the quantum histories.

Detlef Dürr, Dustin Lazarovici

Leonardo Castellani

It is convenient to describe a quantum system at all times by means of a “history operator” [Formula: see text], encoding measurements and unitary time evolution between measurements. These operators naturally arise when computing the probability of measurement sequences, and generalize the “sum over position histories” of the Feynman path-integral. As we argue in this work, this description has some computational advantages over the usual state vector description, and may help to clarify some issues regarding nonlocality of quantum correlations and collapse. A measurement on a system described by [Formula: see text] modifies the history operator, [Formula: see text], where [Formula: see text] is the projector corresponding to the measurement. We refer to this modification as “history operator collapse”. Thus, [Formula: see text] keeps track of the succession of measurements on a system, and contains all histories compatible with the results of these measurements. The collapse modifies the history content of [Formula: see text], and therefore modifies also the past (relative to the measurement), but never in a way to violate causality. Probabilities of outcomes are obtained as [Formula: see text]. A similar formula yields probabilities for intermediate measurements, and reproduces the result of the two-vector formalism in the case of the given initial and final states. We apply the history operator formalism to a few examples: entangler circuit, Mach–Zehnder interferometer, teleportation circuit and three-box experiment. Not surprisingly, the propagation of coordinate eigenstates [Formula: see text] is described by a history operator [Formula: see text] containing the Feynman path-integral.